Hi Andy,
I always have a 3 step process I gop through when these sorts of things happen.

1. restart
2. reinstall (you've done this)
3. recreate preferences files. (instructions below)
and sometimes
4. reinstall fonts. They are a pesky thing! The fonts you can trash and reinstall using Font Fixer from the downloads page of the support area on the website are Helena, Rosetta, Yehudit. There are more, but these are the common ones likely to give you problems. You can get Font Book to do a consistency check on your fonts too. That can point out problems. You will generally find the in the ~/Library folder (See below)

To recreate preferences, just drag the "Accordance Preferences" folder onto your desktop. This folder can usually be found in Macintosh HD/Users/{your user name]/Library/Preferences/ It's a folder there, and the easiest way to get there is to option click the Go menu in the Finder (hold the option key down, and select Library in that menu, as it is hidden in Lion and Mountain Lion. Then you will see the Preferences folder - have a look in there.

If it's not there, then double click on your hard disk icon (Usually called Macintosh HD unless you have changed it), open the Library folder you will see there, and then Preferences in that. Again, if that's where the Accordance Preferences folder is, then drag it on to your desktop.

I suggest you do this rather than just trash your preferences because if it makes no difference to the crash behaviour, then you haven't lost all your preferences that you set up previously.

You will have to revalidate your Accordance install if you do this.

Let us know how you go.

Can you reply with your Machine type, OS you are running, and how much memory you have if you need more assistance?

I dragged the Accordance Preference file onto my desktop and opened Accordance. I was immediately prompted to reinstall Accordance. At the time I thought this is what I was supposed to do, but now I think I've made a big mistake. The install set me back to 9.4.3, I lost all my user notes, etc.

When I tried to check for updates, Accordance crashed. It does it every time I check for updates.